Filterbank Multicarrier (FBMC) transmission with Offset Quadrature-Amplitude Modulation (OQAM) is one of the candidate transmission schemes for future wireless system (e.g. 5G). In contrast to state-of-the-art CP-OFDM (cyclic-prefix orthogonal frequency division multiplexing) transmission, which is used in LTE, FBMC/OQAM system is advantageous in the aspects of better controlling the out-of-band radio power leakage and achieving higher spectral efficiency.
In baseband discrete time model, with M subcarriers, we can write the FBMC/OQAM signal at the transmitter side as follows:
                              s          ⁡                      [            t            ]                          =                              ∑                          k              =              0                                      M              -              1                                ⁢                                    ∑                              n                =                                  -                  ∞                                                            +                ∞                                      ⁢                                          c                                  k                  ,                  n                                            ⁢                                                p                                      T                    ,                    k                                                  ⁡                                  [                                      t                    -                    nM                                    ]                                                                                        (        1        )            Where pT,k [t] is the frequency shift version of prototype filter pT[t]:
                                          p                          T              ,              k                                ⁡                      [            t            ]                          =                                            p              T                        ⁡                          [              t              ]                                ⁢                      e                          j              ⁢                                                2                  ⁢                  π                                M                            ⁢                              k                ⁡                                  (                                      t                    -                    D                                    )                                                                                        (        2        )            Here ck,n is complex symbol (OQAM symbol) and can be represented as follows:ck,n=dk,2nejφk,2n+dk,2n+1ejφk,2n+1  (3)
Within such equation, dk,n represent real valued symbol (PAM symbol) and the additional phase term φk,n is aimed to add i alternatively in time as well as in frequency domain to contrast OQAM symbols. One example follows:φk,n=(π/2)(k+n)  (4)Hence, for simplicity, we can rewrite FBMC/OQAM signal at the transmitter side:
                                                                        s                ⁡                                  [                  t                  ]                                            =                            ⁢                                                ∑                                      k                    =                    0                                                        M                    -                    1                                                  ⁢                                                      ∑                                          n                      =                                              -                        ∞                                                                                    +                      ∞                                                        ⁢                                                            d                                              k                        ,                        n                                                              ⁢                                          e                                              j                        ⁢                                                                                                  ⁢                                                  φ                                                      k                            ,                            n                                                                                                                ⁢                                                                  p                        T                                            [                                              t                        -                                                  n                          ⁢                                                      M                            2                                                                                              ]                                        ⁢                                          e                                              j                        ⁢                                                                              2                            ⁢                            π                                                    M                                                ⁢                                                  k                          ⁡                                                      (                                                          t                              -                              D                                                        )                                                                                                                                                                                                                      =                            ⁢                                                ∑                                      k                    =                    0                                                        M                    -                    1                                                  ⁢                                                      ∑                                          n                      =                                              -                        ∞                                                                                    +                      ∞                                                        ⁢                                                            d                                              k                        ,                        n                                                              ⁢                                                                  r                                                  k                          ,                          n                                                                    ⁡                                              [                        t                        ]                                                                                                                                                    (        5        )                        With                                                                            r                          k              ,              n                                ⁡                      [            t            ]                          =                                            p              T                        [                          t              -                              n                ⁢                                  M                  2                                                      ]                    ⁢                      e                          j              ⁢                                                2                  ⁢                  π                                M                            ⁢                              k                ⁡                                  (                                      t                    -                    D                                    )                                                              ⁢                                    e                              j                ⁢                                                                  ⁢                                  φ                                      k                    ,                    n                                                                        .                                              (        6        )            
Thus, FBMC/OQAM signal can be treated as PAM modulated signal. Please note that, in this disclosure, we choose the PAM symbol models for presentation.
Assuming prototype filter being symmetrical and real-valued, the real field orthogonality is fulfilled as follows:Re{Σt=−∞+∞rk′n′[t]r*k n[t]}=δk,k′δn,n′  (7)Re{.} returns the real part of a complex number.
For MIMO-Alamouti transmission (Alamouti is a special case of space-time or space-frequency block code (abbreviated as STBC/SFBC in this disclosure), which is proposed by Alamouti in 1990s), however, it is very difficult for FBMC modulation schemes to combine the Alamouti Max-Ratio-Combing (MRC) decoder to fully achieve the antenna transmit diversity, since the complex field orthogonality requirement of Alamouti-MRC decoder cannot be fulfilled by FBMC.
More specifically, in Alamouti two complex (or real) symbols are transmitted as follows:                Antenna 1: [d1, −d2*]        Antenna 2: [d2, d1*].        
If in case the complex field orthogonality is fulfilled by the modulation, the corresponding received data block [r1, r2] can be denoted as:r1=h1d1+h2d2+n1  (8)r2=h1d2*+h2d1*+n2  (9)Here h1 and h2 denotes channel coefficients.
After Alamouti demapping at the receiver side, we observe:{tilde over (d)}1=h1*r1+h2r2*=(|h1|2+|h2|2)d1+ñ1  (10){tilde over (d)}2=h2*r1−h1r2*=(|h1|2+|h2|2)d2+ñ2  (11)Hence, two transmitted symbols are recovered achieving full transmit diversity.
When Alamouti is applied in an FBMC system, note that only real field orthogonally is fulfilled by FBMC. Thus, aforementioned MRC decoding cannot completely remove the interference between antennas. This fact will result in introducing interference on each modulated symbol and thus FBMC-Alamouti mapping inacceptable in any application. In the past a lot of effort has been made to solve this problem. However, so far there is no satisfying solution which can effectively cancel this inherent interference, even in flat fading channels.